Suppose for some region R in the xy-plane integral integral_R f(x, y)dA = 0. If

Question

Suppose for some region R in the xy-plane integral integral_R f(x, y)dA = 0. If ft is subdivided into two regions R_1 and R_2 that do not overlap (except at maybe their boundaries) then integral integral_R f(x, y)dA = -integral integral_R f(x, y) dA. (b) The area of the region R in the xy-plane is given by integral integral_R xy dA. (c) For the function f(x, y) = ax + by, the area of the surface z = f(x, y) over a rectangle R in the xy-plane is the product of |(1, 0, a) times (0, 1, 6|1 and the area of R. (d) If E is the unit ball x^2 + y^2 + z^2 lessthanorequalto 1, then integral integral integral_E z dV = 0. (e) (r, theta) and (-r, theta + pi) are polar coordinates of the same point.

Explanation / Answer

a)TRUE

b)TRUE

c)TRUE

d)true

e)TRUE

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